Related papers: Internal noise interference to warnings of tipping…

We study the dynamics of a simple adaptive system in the presence of noise and periodic damping. The system is composed by two paths connecting a source and a sink, the dynamics is governed by equations that usually describe food search of…

We consider stochastic partial differential equations (SPDEs) on the one-dimensional torus, driven by space-time white noise, and with a time-periodic drift term, which vanishes on two stable and one unstable equilibrium branches. Each of…

We prove for an infinite array of globally coupled overdamped anharmonic oscillators subject to additive Gaussian white noise the existence of a well-behaved critical manifold in the parameter space which separates a symmetric phase from a…

Theoretical models that describe oscillations in biological systems are often either a limit cycle oscillator, where the deterministic nonlinear dynamics gives sustained periodic oscillations, or a noise-induced oscillator, where a fixed…

Noise is ubiquitous in various systems. In systems with multiple timescales, noise can induce various coherent behaviors. Self-induced stochastic resonance (SISR) is a typical noise-induced phenomenon identified in such systems, wherein…

Transformers have revolutionized deep learning across various domains but understanding the precise token dynamics remains a theoretical challenge. Existing theories of deep Transformers with layer normalization typically predict that…

We consider the influence of stochastic perturbations on stability of a unique positive equilibrium of a difference equation subject to prediction-based control. These perturbations may be multiplicative $$x_{n+1}=f(x_n)-\left( \alpha +…

In recent years, material-induced noise arising from defects has emerged as an impediment to quantum-limited measurement in systems ranging from microwave qubits to gravity wave interferometers. As experimental systems push to ever smaller…

We consider a class of models describing an ensemble of identical interacting agents subject to multiplicative noise. In the thermodynamic limit, these systems exhibit continuous and discontinuous phase transitions in a, generally,…

This paper concerns stochastic perturbations of piecewise-smooth ODE systems relevant for vibro-impacting dynamics, where impact events constitute the primary source of randomness. Such systems are characterised by the existence of…

The dynamics of an ensemble of bistable elements under the influence of noise and with global time-delayed coupling is studied numerically by using a Langevin description and analytically by using 1) a Gaussian approximation and 2) a…

We consider the stochastic patterns of a system of communicating, or coupled, self-propelled particles in the presence of noise and communication time delay. For sufficiently large environmental noise, there exists a transition between a…

The performance and scalability of semiconductor quantum-dot (QD) qubits are limited by electrostatic drift and charge noise that shift operating points and destabilize qubit parameters. As systems expand to large one- and two-dimensional…

This work proposes a general framework for capturing noise-driven transitions in spatially extended non-equilibrium systems and explains the emergence of coherent patterns beyond the instability onset. The framework relies on stochastic…

We consider a model for systemic risk comprising of a system of diffusion processes, interacting through their empirical mean. Each process is subject to a confining double-well potential with some uncertainty in the coefficients,…

We study the limiting dynamics of a large class of noisy gradient descent systems in the overparameterized regime. In this regime the set of global minimizers of the loss is large, and when initialized in a neighbourhood of this zero-loss…

A prototype model of a stochastic one-variable system with a linear restoring force driven by two cross-correlated multiplicative and additive Gaussian white noises was considered earlier [S. I. Denisov et al., Phys. Rev. E 68, 046132…

We develop a formalism to describe the discrete-time dynamics of systems containing an arbitrary number of interacting species. The individual-based model, which forms our starting point, is described by a Markov chain, which in the limit…

In oscillatory reaction-diffusion systems, time-delay feedback can lead to the instability of uniform oscillations with respect to formation of standing waves. Here, we investigate how the presence of additive, Gaussian white noise can…

The paradigm of learning from automatic annotations driven by pre-trained experts and Foundation Models dominates data-hungry applications. However, it introduces a critical challenge: model-induced label noise. Unlike stochastic noise in…